A few months back a friend of a friend of mine had a very unpleasant Lyft ride. Just before she was home, her driver started asking about her relationship status and eventually slowed down the car and locked the doors. She freaked out and and he eventually let her out. She reported it to Lyft but they said it was very little to do as it was her word against his. I've also read about similar stories in social media about ride sharing services so I personally don't think Uber/Lyft is that safe for a woman.

I guess you're not 100% safe in a taxi either but afaik they run more extensive background checks than Lyft/Uber. Honestly, I can't blame the mother of your GF for being a bit over protective in this case.